Generating -Commutator Identities and the -BCH Formula

Table 1

A few numbers relative to the analysis of the identities obtained by our procedure, for -centered -mutators of total degree ≤ 10.

Bidegree	()	()	()	I()	R()	A()	B()	C()
	1	1	0	0	0	0	0	0
	2	2	0	0	0	0	0	0
	4	3	1	0	1	0	0	0
	8	5	3	0	0	1	1	1
	8	4	4	2	2	0	0	0
	24	9	15	8	2	2	2	1
	16	5	11	8	3	0	0	0
	64	14	50	38	5	3	3	1
	96	19	77	60	6	5	5	1
	32	6	26	22	4	0	0	0
	160	20	140	122	9	4	4	1
	320	34	286	254	13	9	9	1
	64	7	57	52	5	0	0	0
	384	27	357	332	14	5	5	1
	960	55	905	852	24	14	14	1
	1280	69	1211	1144	28	19	19	1
	128	8	120	114	6	0	0	0
	896	35	861	828	20	6	6	1
	2688	83	2605	2524	40	20	20	1
	4480	125	4355	4232	54	34	34	1
	256	9	247	240	7	0	0	0
	2048	44	2004	1962	27	7	7	1
	7168	119	7049	6932	62	27	27	1
	14336	209	14127	13920	96	55	55	1
	17920	251	17669	17420	110	69	69	1

For every bidegree we have the following.
(): number of symbolic -centered -mutators of bidegree .
(): dimension of the vector space .
(): number of relations among the symbolic -mutators.
I(): number of inherited relations (I).
R(): number of relations according to Reiner’s identity (R).
A(): number of relations according to identity (A).
B(): number of relations according to identity (B).
C(): number of relations according to procedure (C).